The number of conditions for a Runge-Kutta method to have effective order \(p\)

DOI10.1016/S0168-9274(96)00028-1zbMath0867.65039OpenAlexW2073477729MaRDI QIDQ5961736

John C. Butcher, Jesús María Sanz-Serna

Publication date: 26 February 1997

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(96)00028-1

zbMATH Keywords

Runge-Kutta methodorder conditionseffective order\(B\)-seriesrooted trees

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (9)

Word series for dynamical systems and their numerical integrators ⋮ Palindromic 3-stage splitting integrators, a roadmap ⋮ Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrödinger Equation ⋮ A New Optimality Property of Strang’s Splitting ⋮ Algebraic structures of B-series ⋮ Unnamed Item ⋮ High order numerical integrators for differential equations using composition and processing of low order methods ⋮ Order and effective order ⋮ Formal series and numerical integrators. I: Systems of ODEs and symplectic integrators

Cites Work

• Improved Trotter-like formula
• A numerical algorithm for Hamiltonian systems
• Canonical \(B\)-series
• Explicit Symplectic Integrators Using Hessian--Vector Products
• Solving Ordinary Differential Equations I
• Symplectic Methods Based on Decompositions
• An Algebraic Theory of Integration Methods
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